Best Arm Identification (BAI) problems are progressively used for data-sensitive applications, such as designing adaptive clinical trials, tuning hyper-parameters, and conducting user studies to name a few. Motivated by the data privacy concerns invoked by these applications, we study the problem of BAI with fixed confidence under ϵ-global Differential Privacy (DP). First, to quantify the cost of privacy, we derive a lower bound on the sample complexity of any δ-correct BAI algorithm satisfying ϵ-global DP. Our lower bound suggests the existence of two privacy regimes depending on the privacy budget ϵ. In the high-privacy regime (small ϵ), the hardness depends on a coupled effect of privacy and a novel informationtheoretic quantity, called the Total Variation Characteristic Time.

This paper investigates the asymptotic distribution of the maximum-likelihood estimate (MLE) in multinomial logistic models in the high-dimensional regime where dimension and sample size are of the same order. While classical largesample theory provides asymptotic normality of the MLE under certain conditions, such classical results are expected to fail in high-dimensions as documented for the binary logistic case in the seminal work of Sur and Candès [2019]. We address this issue in classification problems with 3 or more classes, by developing asymptotic normality and asymptotic chi-square results for the multinomial logistic MLE (also known as cross-entropy minimizer) on null covariates. Our theory leads to a new methodology to test the significance of a given feature. Extensive simulation studies on synthetic data corroborate these asymptotic results and confirm the validity of proposed p-values for testing the significance of a given feature.

Though achieving excellent performance in some cases, current unsupervised learning methods for single image denoising usually have constraints in applications. In this paper, we propose a new approach which is more general and applicable to complicated noise models. Utilizing the property of score function, the gradient of logarithmic probability, we define a solving system for denoising. Once the score function of noisy images has been estimated, the denoised result can be obtained through the solving system. Our approach can be applied to multiple noise models, such as the mixture of multiplicative and additive noise combined with structured correlation. Experimental results show that our method is comparable when the noise model is simple, and has good performance in complicated cases where other methods are not applicable or perform poorly.

Advances in high-throughput sequencing technology have led to significant progress in measuring gene expressions at the single-cell level. The amount of publicly available single-cell RNA-seq (scRNA-seq) data is already surpassing 50M records for humans with each record measuring 20,000 genes. This highlights the need for unsupervised representation learning to fully ingest these data, yet classical transformer architectures are prohibitive to train on such data in terms of both computation and memory. To address this challenge, we propose a novel asymmetric encoder-decoder transformer for scRNA-seq data, called xTrimoGeneα (or xTrimoGene for short)4, which leverages the sparse characteristic of the data to scale up the pre-training. This scalable design of xTrimoGene reduces FLOPs by one to two orders of magnitude compared to classical transformers while maintaining high accuracy, enabling us to train the largest transformer models over the largest scRNA-seq dataset today. Our experiments also show that the performance of xTrimoGene improves as we scale up the model sizes, and it also leads to SOTA performance over various downstream tasks, such as cell type annotation, perturb-seq effect prediction, and drug combination prediction.